[EM] Meta-criteria 6 of 9: Heuristics. #1, simplicity

[Juho]

On May 7, 2010, at 7:11 PM, Kristofer Munsterhjelm wrote:

> Juho wrote:
>
>> One could discuss which rule should apply in those special cases  
>> when both criteria can not be met. In order to determine exactly  
>> when we have true clones in our hands we would need to have the  
>> original votes, and also the preference strengths to know if the  
>> candidates are closely related or not. (Actually also near clones  
>> should be treated as clones since we can not expect that all voters  
>> treat those candidates as clones.) The pairwise matrix contains  
>> only partial information. If we make a method 100% clone proof  
>> using the matrix information only we can not limit to the clone  
>> cases only but we are bound to influence the result also in other  
>> cases. One pairwise matrix can be obtained both from votes that  
>> have clones and from votes that do not have clones. It is for  
>> example possible that no voter ranks together those candidates that  
>> we must now deem to be (potential) clones since there is a  
>> possibility that in some other vote set they could be clones. The  
>> Schulze method uses path heuristics to eliminate all cases where  
>> clones could exist and influence the end result.
>> (Are there other strong reasons behind the use of paths? In real  
>> life the existence of the long beat paths maybe doesn't refer to  
>> any natural key target.)
>
> Schulze's primary argument is that the use of paths let one make a  
> method that is very close to Minmax, yet is cloneproof and elects  
> from Smith. Thus, if one thinks the Minmax yardstick is a good one,  
> yet that Minmax's clone susceptibility means one has to diverge from  
> it in certain cases, Schulze is a good method.

Yes, Schulze has some such properties. If both criteria are considered  
important, then one should just estimate which method is closer to  
ideal. Minmax may ignore clones that have strong losses to each others  
(it puts more weight on the distance to being a Condorcet winner).  
Path based methods may defend "clones" also when there are no clones  
(and a candidate that meets neither criterion might win).

>
> As for your second part, there is naturally a tradeoff between  
> strong paths and short paths. Schulze considers paths equally no  
> matter their length, but the question is sensible. Methods that  
> focus on short paths are more like Copeland (which focuses on  
> "paths" of a single step), and methods that elect from the uncovered  
> set would have short paths from the winners to the candidates not in  
> the uncovered set.

I see the "one step philosophy" as answering to question "if we would  
elect x, would the society be happy with x or would it be interested  
in changing candidate x to someone else" (not on questions on if the  
society would be interested in multiple sequential changes). The  
philosophy of Copeland's method would make sense in principle. I guess  
the minmax philosophy can be said to focus only on the strength of the  
losses and not on the number of them because of the clone related  
problems that Copeland has. The number of losses also has no meaning  
if the intention is to check how close each candidate is to being a  
Condorcet winner.

Juho